Step by step
The question
Question: work out (4 × 10³) × (5 × 10⁴).
(4 × 103) × (5 × 104)
1 Group the parts
Times can go in any order.
So we put the numbers together, and the powers of 10 together.
= 4 × 5 × 103 × 104
2 Work out each part
4 times 5 is 20.
4 × 5 = 20
We write 20 for the numbers.
= 20 × 103 × 104
The rule: same base, times, add the powers.
3 plus 4 is 7.
103 × 104 = 103 + 4 = 107
Now we have 20 × 10⁷.
= 20 × 107
3 Fix the number
20 is not under 10.
20 is 2 times 10, that is 2 × 10¹.
20 = 2 × 101
We write 2 × 10¹ in place of 20.
= 2 × 101 × 107
Add the powers: 1 plus 7 is 8.
101 × 107 = 101 + 7 = 108
So the answer is 2 × 10⁸.
= 2 × 108
4 Check
Let's check the answer is in scientific notation.
2 is from 1 to under 10, and it is times a power of 10.
Yes!
2 is from 1 to under 10, times 108
Let's look back.
First: group the parts.
Then: work out each part.
Then: fix the number.
Last: check.
Answer
= 2 × 108